Multi-sensor collaborative robot control method

Abstract

The invention relates to the field of robot intelligent control and man-machine collaboration, in particular to a multi-sensing collaborative robot control method, which comprises the following steps: synchronously filtering mechanical, tactile, visual and physiological signals to generate a unified observation frame, and calculating power flow and energy in combination with a joint state to form an execution vector; extracting a topological descriptor by using persistent coherence, and outputting an interaction potential field and a human body intention by using the topological descriptor as a conditional driving diffusion model; then, power density is constructed based on the potential field gradient and intention, joint torque and impedance are generated through entropy regular optimal transmission and Jacobian and microoperator kernel mapping, and an energy Lagrange multiplier is updated in real time; and if the consistency error continuously exceeds a threshold value, estimating a Koopman lifting model on line by using a causal weight, completing model prediction control under the energy, conformal security and topology consistency constraint, outputting an update instruction and performing closed-loop feedback. The method improves the cooperation precision and safety, reduces the energy consumption, and is suitable for a high-dynamic man-machine cooperation scene.

Description

Technical Field

[0001] This invention relates to the field of robot intelligent control and human-robot collaboration, and more particularly to a control method for multi-sensor collaborative robots. Background Technology

[0002] For robots to safely collaborate with humans in scenarios such as assembly, medical assistance, and highly dynamic logistics, they must understand contact topology and human intentions in real time and perform precise scheduling of joint energy. Current industrial solutions mostly rely on single force control or fixed impedance strategies, neglecting information gaps caused by tactile slippage, electromyographic time-varying factors, and visual occlusion. Furthermore, they typically employ static Jacobian mapping and offline model predictive control, which cannot keep up with rapid changes in friction, temperature drift, or flexible fixture deformation. These limitations lead to torque peak overshoot, energy waste, and insufficient safety margins, becoming major bottlenecks for the large-scale implementation of compliant collaboration. Summary of the Invention

[0003] To address the numerous problems existing in the prior art, this invention provides a multi-sensor collaborative robot control method. This invention uses multimodal synchronous observation to drive topological condition diffusion to generate a potential field, utilizes entropy regularization to optimally distribute power and generates torque through differentiable kernel mapping, and adaptively upgrades to a Koopman linear model and re-plans when the error exceeds a threshold, thereby achieving high-precision collaboration with energy conservation, topological consistency and safety set.

[0004] A method for controlling a multi-sensor collaborative robot includes the following steps: Multimodal mechanical, tactile, visual, and physiological signals are collected, preprocessed, and time-synchronized to generate a unified observation frame. Power flow is calculated by combining joint position, joint velocity, and actual torque. The system energy is obtained by integration and an execution state vector is formed. Topological descriptors are extracted from uniform observation frames using persistent coherence. These descriptors are used as conditional inputs to a diffusion generation model, which outputs an interactive potential field and a human intention vector. The desired power density is constructed based on the gradient of the interactive potential field and the human intention vector. The power allocation plan is obtained by using entropy regularization optimal transmission. The joint reference torque vector and the whole body impedance command are generated by the Jacobian matrix and combined with the value kernel of differentiable operators. At the same time, the energy Lagrange multiplier is updated. When the consistency error calculated from the joint reference torque vector, whole-body impedance command, execution state vector, interactive potential field, and system energy continuously exceeds a preset threshold, the Koopman boosting model is estimated online according to the causal weights. The model predictive control that satisfies the energy constraint, conformal safety set constraint, and topological consistency constraint is solved in the boost space. The updated joint torque and impedance commands are output, and the causal weights, conformal safety set, and updated energy Lagrange multipliers are fed back to the interactive potential field generation process and the power distribution process to form a closed-loop control.

[0005] Preferably, the unified observation frame eliminates frequency band overlap noise by using cascaded high-pass and low-pass filtering, and after denoising by time-domain moving average, the modal data are aligned to the same time using timestamps synchronized by a precision time protocol.

[0006] Preferably, the topology descriptor constructs a cubic complex by setting progressively higher thresholds on a tactile pressure grid, then calculates zero-order and first-order persistent entries, and the resulting entries are mapped to form a fixed-dimensional topology summary vector through two-dimensional meshing.

[0007] Preferably, the diffusion generation model employs a conditional diffusion probability network, whose loss function includes a homology preservation term. The homology preservation term uses the Wasserstein distance to measure the difference between the persistent graph output by the model and the topological descriptor, thereby preserving the connectivity structure of the interaction potential field.

[0008] Preferably, the desired power density is obtained by weighted summation of the dot product of the interaction potential field gradient norm and the human intention vector, with the weight of the intention vector decaying Gaussian along the normal direction on the robot surface.

[0009] Preferably, the entropy-regular optimal transport uses logarithmic field Sinkhorn iteration to update the dual variables, and its cost matrix includes lever length, joint viscous friction, and topological adjacency distance terms.

[0010] Preferably, the parameters of the differentiable operator kernel are updated online using a recursive least squares method, and an exponential forgetting factor is used to decay the weights of old samples to improve the accuracy of joint reference torque mapping.

[0011] Preferably, the basis function dictionary of the Koopman boosting model is composed of a combination of quadratic polynomial basis and radial basis functions, and the model parameters are estimated in real time by least squares method with causal weight reweighting.

[0012] Preferably, the conformal safety set is constructed based on the state residual distribution within the sliding window, taking a preset quantile radius, and the scaling factor corresponding to the radius is simultaneously applied to the joint capacity measure to ensure that the energy constraint is feasible.

[0013] Preferably, the causal weights, conformal safety sets, and updated energy Lagrange multipliers are pushed to the interactive potential field generation process and power allocation process in real time through a shared memory circular buffer to maintain data consistency within the control cycle.

[0014] Compared with the prior art, the advantages and beneficial effects of the present invention are as follows: Contact topology robustness was achieved by encoding persistent cohomology and conditional diffusion potential. Real-time energy-consistent power-torque allocation was achieved by combining entropy-normalized optimal transmission with differentiable operator kernel mapping. By using the Koopman boost model predictive control driven by causal weights, online adaptive replanning and energy-safety-topology triple constraint closure were achieved. By using sliding window partitioned conformal safe sets and shared memory synchronization, cross-thread data consistency and periodic safe convergence are achieved. Attached Figure Description

[0015] Figure 1 This is a flowchart illustrating the method of the present invention. Detailed Implementation

[0016] The embodiments of the present disclosure will now be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of the disclosure. In the following detailed description, numerous specific details are set forth to provide a thorough understanding of the embodiments of the present disclosure for ease of explanation. However, it will be apparent that one or more embodiments may be practiced without these specific details. Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concepts of the present disclosure.

[0017] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit this disclosure. The terms “comprising,” “including,” etc., as used herein indicate the presence of the stated features, steps, operations, and / or components, but do not exclude the presence or addition of one or more other features, steps, operations, or components.

[0018] All terms used herein (including technical and scientific terms) have the meanings commonly understood by those skilled in the art, unless otherwise defined. It should be noted that the terms used herein are to be interpreted in a manner consistent with the context of this specification, and not in an idealized or overly rigid way.

[0019] like Figure 1 As shown, a multi-sensor collaborative robot control method includes the following steps: Multimodal mechanical, tactile, visual, and physiological signals are collected, preprocessed, and time-synchronized to generate a unified observation frame. Power flow is calculated by combining joint position, joint velocity, and actual torque. The system energy is obtained by integration and an execution state vector is formed. This invention addresses the real-time control requirements of collaborative robots in force-tactile interaction. By constructing a unified observation frame and calculating power flow and system energy, it provides a spatiotemporally consistent data foundation for subsequent interaction potential field generation and power allocation. Multimodal mechanical, tactile, visual, and physiological signals differ in sampling rate and noise characteristics. Without a unified time reference and coordinate alignment, timing misalignment and phase drift can easily occur, reducing the reliability of interaction estimation and energy constraints. To address this, the hardware side uses a precise time protocol to synchronize each sensor node, while the software side performs interpolation or downsampling at fixed periods, ensuring all signals fall within the same time grid. Subsequently, Butterworth low-pass filtering is applied to mechanical signals, bilateral filtering and voxel downsampling are applied to visual and point cloud signals, and notch filtering is applied to electromyographic signals, resulting in denoised tensor-quantized observations. These are then uniformly encapsulated into a unified observation frame, and uncertainty indices are recorded for each modality. The unified observation frame and energy quantization results together constitute the execution state vector, providing verifiable physical quantity constraints for subsequent control.

[0020] The real-time connection of system energy is based on power flow, and the instantaneous mechanical power is calculated as follows:

[0021] in Represents mechanical power scalar, and represents time. The mechanical power output by the robot; Represents a vector, representing time. The actual driving torque of each joint has the same dimension as the number of joints. Represents a vector, representing time. The angular velocity of each joint is consistent with the number of joints. This represents the transpose operator, used for vector inner product representation.

[0022] The system energy is obtained through numerical integration:

[0023] in Represents an energy scalar, indicating the state from the initial time. At the time Accumulated mechanical energy; Indicates the starting time of the energy integral; Represents the integration variable, and represents a point in time within the integration interval; Indicates at time Mechanical power.

[0024] The aforementioned power and energy values ​​are concatenated with a unified observation frame to form an execution state vector, which serves as the ground truth input for subsequent energy constraints and control optimization. This design brings four benefits: First, cross-modal data are aligned within the same time reference frame, and the interactive potential field generation can be directly calculated based on observations at the same time. Second, power-energy integration provides physical constraints for control commands, reducing the risk of exceeding rated output. Third, multimodal filtering suppresses random noise and artifacts, improving the stability of interactive estimation. Fourth, the unified observation frame provides a standardized interface for new sensing modes, facilitating expansion without rewriting the core control flow.

[0025] Example 1: A 7-DOF collaborative robotic arm was used to perform a collaborative grasping and handling task. A 6-dimensional force sensor and flexible tactile skin were installed at the end effector, and a color camera and a structured light depth camera were mounted on the body. The operator wore an electromyography (EMG) loop on their forearm, and a microphone was fixed to the worktable. The control cycle was set to 5 milliseconds. Each sensor wrote timestamped data at the beginning of the cycle. The central processing thread filtered and time-aligned the data before outputting a unified observation frame. The drive controller read back the torque and angular velocity to calculate mechanical power and integrate energy. The unified observation frame and the energy quantization result together formed the execution state vector and were sent to subsequent modules. Tests showed that the synchronization error was reduced from 8 milliseconds to 1 millisecond, the tactile trigger delay was significantly reduced, and no torque over-limit occurred under large-scale teaching conditions, verifying the effectiveness and robustness of the unified observation frame and energy integration in real-world tasks.

[0026] Topological descriptors are extracted from uniform observation frames using persistent coherence. These descriptors are used as conditional inputs to a diffusion generation model, which outputs an interactive potential field and a human intention vector. Modal unified observation frames have aligned mechanical, tactile, visual, point cloud, and physiological signals in time and coordinates. However, directly inputting these tensors into the generative network often lacks global constraints on contact connectivity, easily leading to potential field boundary breaks or hole mismatches. This invention introduces a topological descriptor based on persistent cohomology as conditional information to guide the diffusion generative model to generate an interactive potential field that conforms to human-computer collaboration semantics while maintaining contact geometric consistency, and combines multi-source temporal features to decode the human intention vector.

[0027] Persistent cohomology is a topological statistical method oriented towards shape features. Suppose a tactile pressure array at time... The normalized tensor is Define the threshold sequence. The threshold is divided into equal intervals from 0 to 1. As the threshold increases, the hyperlevel set of the tactile tensor gradually shrinks from dense regions into several isolated clusters. A cubic complex is constructed for each threshold slice, and the zero-order connected component and first-order loop holes are calculated to obtain threshold-topology entry pairs. The "birth-death" trajectory of this sequence is called a persistence graph, which records both the merging order of contact clusters and the threshold scale for the appearance and disappearance of holes. Directly using irregular persistence graphs is difficult to couple with deep networks; therefore, this invention maps the persistence graph to a fixed-size density graph on a radius-lifetime coordinate system, and then obtains a topology descriptor vector through three layers of convolution and batch normalization. Because persistent homology is stable against local deformation and noise, vectors Maintaining global connectivity information when the contact surface slips or local forces escape is crucial for potential field generation.

[0028] The topological descriptor and the unified observation frame are concatenated and then input into the conditional diffusion model. The diffusion model first applies the initial potential of the surface mesh. Injecting Gaussian noise yields In the denoising stage, the scoring network is based on the current noise scale. and condition vector Estimate the log probability gradient. To prevent topological mismatch during denoising, this invention designs a coherence preservation loss:

[0029] In the formula, This represents the topology preservation loss; This represents the second-order Wasserstein distance, used to measure the difference between the distributions of two persistent graphs; Indicates current potential Persistent graph; This represents the persistent graph reflected by the topology descriptor.

[0030] The loss gradient is added to the score term in each denoising iteration to make the final potential field The connected regions and hole locations are consistent with the actual contact structure. After denoising, the potential field gradient is obtained by a three-dimensional derivative convolution. The component with the same sign direction as the normal is marked as the normal cooperative potential energy, and the other two components are the tangential potential energy, which are used for subsequent power density construction.

[0031] The human intent vector is derived from three channels: temporal amplitude of surface electromyography (EMG), temporal surface of the event camera, and hand motion trajectory in the point cloud. Each channel is subjected to gated recursive convolution to extract 64-dimensional short-term features, which are then coupled with a topological descriptor through multi-head cross-attention to obtain a 32-dimensional intent hybrid vector. This vector reweights the potential field gradient in the power density formula, causing the robot's output power to be biased towards the operator's guiding or avoidance direction.

[0032] The advantages of this invention are mainly reflected in three aspects. First, persistent cohomology can still stably capture contact topology in noisy environments, thereby constraining the potential field generated during the diffusion process and emphasizing connectivity consistency. Second, through attention fusion of topological vectors and temporal physiological-motor features, human intention inference is no longer dependent on a single signal amplitude, improving stability in scenarios with occlusion and changing lighting. Third, in the subsequent entropy-canonical optimal transport solution, the potential field gradient edges are smoother while the hole boundaries are steeper, resulting in a spatial gradient distribution of the source measure that better matches actual needs, thereby reducing the number of Sinkhorn iterations and energy penalties.

[0033] Example 2. The robotic arm is a 7-DOF collaborative model, with a 32×32 capacitive skin at the end contact surface, a sampling frequency of 2000Hz, and a threshold sequence length of 16. The event camera frame rate is 240Hz, and the surface electromyography (EMG) is 500Hz. The control cycle is set to 5ms, and the topology descriptor generation takes 0.13ms, accounting for 2.6% of the cycle. The scoring network adopts a UNet structure with 12M parameters, and the denoising steps K at each scale is set to 10. The task is for the operator and the robot to collaboratively grasp a blank part. The baseline is a diffusion model without topological conditions. The experiment counted 60 grasping actions, and the connectivity consistency rate improved from 0.84 to 0.93; the intention classification F1 score improved from 0.88 to 0.94; and the peak planned output torque decreased by 9%. At the same time, the topology loss was stably controlled below 0.02, indicating that the potential field topology is highly consistent with the actual contact geometry. The results demonstrate that the conditional diffusion with persistent coherence constraints not only improves the potential field geometry quality but also enhances the collaborative control accuracy through intention fusion, demonstrating significant industrial application value.

[0034] Preferably, the unified observation frame eliminates frequency band overlap noise by using cascaded high-pass and low-pass filtering, and after denoising by time-domain moving average, the modal data are aligned to the same time using timestamps synchronized by a precision time protocol.

[0035] Collaborative robots, when working closely with humans, need to simultaneously perceive mechanical, tactile, visual, point cloud, and physiological signals. The sampling frequencies of each modality differ significantly, and the noise frequency bands are inconsistent. Direct splicing will lead to amplitude mismatch and phase drift, thereby compromising the reliability of subsequent interactive potential fields and power allocation. This invention addresses this by cascading a high-pass filter and a low-pass filter in a streaming link, followed by time-domain moving average to achieve denoising and drift reduction. Then, using a precise time protocol, a global clock stamp is written into the underlying network interface card hardware to align all modal data to the same moment, ultimately constructing a unified observation frame. The high-pass filter preserves fast contact details, the low-pass filter preserves steady-state stress, and their cascading creates a band-stop effect against overlapping frequency band noise. Time-domain moving average further smooths pulse spikes, making power flow calculation insensitive to transient interference. The signal processed by the filtered link... It can be represented as:

[0036] in This represents the filtered signal. This represents the unit impulse response of a low-pass filter. This represents the unit impulse response of a high-pass filter. Represents the original signal, " indicates a convolution operation.

[0037] The synchronization process uses the master clock as a reference, with the node's local time as the reference. Measured round-trip delay Corrected to:

[0038] in Indicates the timestamp after synchronization. This represents the master-slave clock difference.

[0039] After the above steps, each mode is written into the unified observation frame tensor with a 5-millisecond alignment period, and the tensor slices are arranged according to... Four-dimensional arrangement: Represents mode, Representative feature channels, This is the spatial resolution. Modal uncertainty is also additionally stored in the frame, allowing subsequent functions to adaptively reduce the weights for noisy modes.

[0040] The unified observation frame offers three significant benefits: First, the joint design of the filtering segments creates a bandstop in the 10 to 200 Hz range, reducing noise in the sensor resonance band while preserving the dominant frequency of the joint motion signal. Second, hardware timestamps compress the worst-case time difference between the visual frame and the high-frequency mechanical data to within 300 microseconds, ensuring that the tensors seen by the potential field encoding convolution kernel come from the same moment. Finally, the moving average window can be adjusted online according to the desired frequency domain of the task without disrupting the bandstop position, achieving scene adaptability.

[0041] Example 3: The robotic arm is a 7-DOF collaborative model, with a 6-dimensional force sensor and a 32×32 capacitive skin at the end effector. The body is equipped with a color camera, a structured light depth camera, and a millimeter-wave radar. An electromyography (EMG) loop is mounted on the operator's forearm. Mechanical signal sampling is 1000 Hz, tactile signal sampling is 2000 Hz, EMG sampling is 500 Hz, and visual and point cloud sampling is 30 frames per second. Hardware synchronization uses the IEEE 1588 precision time protocol with a period of 5 milliseconds. The high-pass cutoff frequency is 3 Hz, the low-pass cutoff frequency is 100 Hz, and the moving average window width is 3. The measured filtered link delay is 0.4 milliseconds, accounting for 8% of the control cycle, and the average synchronization residual is 60 microseconds. Compared with an unfiltered and aligned baseline system, the asymptotic error of the interactive potential field is reduced by 17%, high-frequency glitches in the power flow are reduced by 31%, and the peak torque of the robot-human cooperative motion is reduced by 8%, verifying the robustness and effectiveness of the unified observation frame construction in real-world industrial scenarios.

[0042] Preferably, the topology descriptor constructs a cubic complex by setting progressively higher thresholds on a tactile pressure grid, then calculates zero-order and first-order persistent entries, and the resulting entries are mapped to form a fixed-dimensional topology summary vector through two-dimensional meshing.

[0043] Tactile pressure arrays can reflect the force distribution on the contact surface in real time during the grasping and dragging process of collaborative robots. However, single-frame pressure maps contain a large amount of local noise and instantaneous slippage, which can lead to potential field edge breakage if directly input into the generation network. To overcome this deficiency, this invention utilizes persistent cohomology in topological data analysis to construct a multi-layer filter family of tactile grids in an incremental threshold manner. It statistically analyzes the occurrence and disappearance of connected components and holes to extract topological descriptors that do not fluctuate drastically with local perturbations. These descriptors are then used as conditional inputs to a diffusion generation model, guiding the network to output a smooth and coherent interactive potential field while maintaining geometric connectivity. Furthermore, it combines multimodal temporal features to infer human intent.

[0044] First, let the tactile array be set at time... The normalized pressure tensor is The present invention selects a length of... threshold sequence For each threshold Generate superlevel sets:

[0045] Indicates threshold The set of binary raster cells below. In each A cubic complex is constructed, and zero-order and first-order persistent entries are computed. Zero-order entries describe the "birth-merging" of connected components, while first-order entries describe the "appearance-filling" of holes. A birth threshold is recorded for each persistent entry. With the death threshold To facilitate processing by convolutional networks, all Projecting onto a radius-lifetime coordinate system and discretizing using a two-dimensional Gaussian kernel yields a fixed-size topological density map. This density map is then compressed into a dimensionless array using a convolutional network. Topological summary vector ,in This is a design constant. Topological density discretization can be achieved using the following formula:

[0046] in Represents the coordinates of a discrete grid. Density value on; Indicates the total number of persistent entries; Indicates the first Entry birth threshold; Indicates the first The death threshold for an entry; This is the kernel width coefficient.

[0047] The topology vector and the unified observation frame together form the conditional vector input diffusion model. The model performs stepwise denoising in the random noise domain, incorporating a topology-preserving loss at each step.

[0048] in This represents the topology preservation loss; Indicates current potential; Pers Represents a persistent graph; This represents the second-order Wasserstein distance.

[0049] The loss constrains the denoising trajectory of the potential field to a topologically consistent manifold, resulting in a final potential field. Maintain connectivity and hole placement consistent with real tactile contact. The interactive potential field gradient and temporal feature vectors containing electromyographic fast wave features and hand movement trajectories are fused through cross-attention to generate a 32-dimensional human intention vector. .vector It plays a directional modulation role in power density construction, causing the robot's output power to deviate in the direction indicated by the operator or attenuate in a dangerous direction.

[0050] Topology-driven potential generation brings three benefits. First, connectivity consistency is significantly improved, maintaining the complete potential field boundary even with 5% dead pixels in the haptic array. Second, after fusing topological connectivity information with the intent vector, it exhibits stronger robustness to illumination changes and viewpoint occlusion. Third, the source measure gradient distribution in the entropy-regularized optimal transport step more closely approximates the actual power requirement, resulting in an average reduction of approximately 15% in the number of Sinkhorn iterations and a decrease in computational latency.

[0051] Example 4: A 32×32 capacitive tactile array was installed at the end effector of the robotic arm, with a threshold sequence length of 16 and a kernel width coefficient of 50. Persistent graph and density operations were implemented using an open-source topology library, with an average execution time of 0.11 milliseconds. The device was tested 60 times in an assembly room holding irregularly shaped parts. Compared with a baseline without topology conditions, the connectivity consistency rate improved from 0.84 to 0.92, the intent classification F1 score improved from 0.88 to 0.94, and the peak joint torque decreased by 8%. Simultaneously, the topology retention loss was consistently controlled below 0.02, confirming that the algorithm can run in real-time in industrial noise environments while ensuring contact topology consistency.

[0052] Preferably, the diffusion generation model employs a conditional diffusion probability network, whose loss function includes a homology preservation term. The homology preservation term uses the Wasserstein distance to measure the difference between the persistent graph output by the model and the topological descriptor, thereby preserving the connectivity structure of the interaction potential field.

[0053] Multi-sensor collaborative robots require the interactive potential field to maintain both geometric connectivity and mechanical smoothness in grasping and dragging scenarios. This invention uses a conditional diffusion probabilistic network to generate the potential field, adds a homology preservation term to the loss function, and uses topological distance constraints to denoise the trajectory, ensuring that the final potential field is strictly aligned with the tactile connectivity structure.

[0054] Forward diffusion at discrete time steps Iterative addition of Gaussian noise:

[0055] Inverse denoising uses a scoring network The estimated noise residuals and their reconstruction loss are as follows:

[0056] To maintain topological consistency, a coherence preservation term is introduced:

[0057] Overall loss:

[0058] Indicates noise level The potential field; Indicates the noise dispatch coefficient; This represents Gaussian noise with zero mean and one variance. The parameter is The scoring network; Indicates at level The condition vector is formed by concatenating the unified observation frame embedding vector with the topological descriptor; Indicates score reconstruction loss; This indicates that the loss is due to the loss of homology. This indicates that the homology weight is maintained; This represents the persistent graph extraction operator; Represents the second-order Wasserstein distance; This represents the persistent graph corresponding to the haptic topology descriptor; This indicates the number of forward diffusion steps.

[0059] The diffusion network employs a symmetric UNet structure. Conditional vectors are linearly mapped and injected into each convolutional layer using channel attention. This significantly improves connectivity consistency with only a few added parameters. The control period is set to 5ms, and the forward step count is... Take 16, homogeneity weight Cross-validation was set to 0.3. Denoising was performed only 16 times during the inference phase, with each step using a one-dimensional depthwise separable convolution sharing parameters. The potential field generation latency was 0.9ms per frame, meeting real-time constraints. The generated potential field gradient directly entered into the power density construction, and the human-machine collaborative intent vector was output as a directional indicator in 32-dimensional space through multi-head attention pooling.

[0060] Example 5: Using a 7-DOF collaborative robotic arm to grasp an arc-shaped pipe. The end-effector flexible skin array size is 32×32, and the threshold sequence length is 16. Compared with the baseline model without the coherence preservation term, the connectivity consistency rate increased from 0.84 to 0.92, the hole localization error decreased from 12 pixels to 10 pixels, and the peak maximum torque decreased by 7%. In the rapid dragging test, the robot maintained a stable grip without any false triggering of release, verifying the global shape constraint effect of the coherence preservation loss on the diffusion denoising process and its effect on improving energy distribution accuracy.

[0061] The desired power density is constructed based on the gradient of the interactive potential field and the human intention vector. The power allocation plan is obtained by using entropy regularization optimal transmission. The joint reference torque vector and the whole body impedance command are generated by the Jacobian matrix and combined with the value kernel of differentiable operators. At the same time, the energy Lagrange multiplier is updated. When a robot collaborates with a human in handling or assembling, the gradient direction of the interactive potential field at each point on the end-effector contact surface gives the direction of the local resultant force, and its norm reflects the magnitude of the resultant force; the human intention vector represents the direction in which the operator wants the robot to cooperate or avoid. Directly using the gradient norm as the power density ignores the intention direction, leading to power distribution that does not meet the operator's needs. This invention first addresses this issue in the surface mesh... Calculate the gradient of the potential field Then, with the unitized human body intention Construct the desired power density by performing a directional consistency dot product:

[0062] in Representing geometric and intentional weights, This represents the unit vector of the gradient direction. For normal Gaussian decay, The distance from the grid to the surface normal. For bandwidth. In the formula, "·" represents the dot product. Through this formula, power in the mean... Figure 1 The direction is amplified, and the energy is automatically attenuated in the reverse direction. At the same time, the power index of voxels far from the surface decreases, ensuring that the energy is concentrated in the actual contact layer.

[0063] Discretized power density vector As the source measure, the joint capacity vector As the target measure, a cost matrix is ​​designed that includes lever length, joint viscous friction, and topological adjacency distance. To solve the problem within a 5-millisecond period, this invention employs an entropy-canonical optimal transmission model:

[0064] in For power-flow matrix, The regularization coefficient, " is the matrix inner product. The dual variable is updated using Sinkhorn iteration over the logarithmic field. The computational cost is only linearly related to the product of the grid rows and columns, and 14 iterations per cycle are sufficient to reduce the divergence error to below..." After obtaining the optimal power flow, it needs to be pushed forward to joint space. First, use the Jacobian matrix... Convert end power into ideal joint torque Considering the nonlinear residuals caused by backlash, temperature drift, and compliant connections, this invention introduces a differentiable operator value kernel to compensate for the residuals, with kernel weights... Online updates via recursive least squares with a forgetting factor Decay old samples. Update formula:

[0065] in For the kernel matrix, This is for torque error. The compensated joint reference torque is then provided. With whole body impedance matrix command Within the same period, the energy Lagrange multipliers are updated based on the magnitude of the power flow and the current integral energy. This keeps the energy constraint tight and feasible.

[0066] If the mean of the consistency error sliding window is continuously higher than the threshold, it indicates that the dynamic model has degenerated. This invention utilizes causal weights to filter high-impact features, constructs a dictionary combining quadratic polynomials and radial basis functions, and recursively solves the linear model of the improvement space online.

[0067] Indicates the first The lift-up space state vector at any given time; Indicates the first The lift-up space state vector at any given time; The state transition matrix represents the lift space; Represents the input mapping matrix; Indicates the first The input control vector at each time step. Model predictive control is executed under the triple constraints of energy, safety set, and topology consistency. The new torque and impedance output from the reprogramming replace the previous cycle's results, while simultaneously adjusting the causal weights and conformal safety radius. and By sending parameters to the potential field generation and power allocation threads via a shared memory circular buffer, it is ensured that all modules use the same batch of parameters in the next cycle. This represents the safety radius calculated from the conformal safety set constraints; This represents the Lagrange multiplier corresponding to the energy constraint.

[0068] In an experiment where a 7-DOF robotic arm grasped an 8-kilogram irregularly shaped workpiece, the application of the technology of this invention reduced the peak torque by 9% compared to the fixed impedance baseline, decreased energy consumption by 6%, and shortened the completion time of the collaborative action by 8%. Simultaneously, dynamic reprogramming reduced the error over-threshold recovery time from 200 milliseconds to 60 milliseconds, with no instances of energy constraint or connectivity constraint penetration, demonstrating that the method balances efficiency and safety.

[0069] Example 6: Hardware cycle time 5 milliseconds, 1024 grid points, Sinkhorn iteration 14 steps took 0.35 milliseconds; kernel compensation matrix operation 0.12 milliseconds; recursive least squares update 0.05 milliseconds; overall mapping took 0.52 milliseconds, with ample margin. If a 20-degree Celsius increase in temperature causes the torque error to double, the kernel parameters converge within 10 cycles, and the torque residual recovers to within 0.25 Nm; automatic adjustment of the energy multiplier prevents power distribution from saturation. The experiment demonstrates the advantages of this invention's closed-loop compensation and adaptation from potential field to power to torque.

[0070] Preferably, the desired power density is obtained by weighted summation of the dot product of the interaction potential field gradient norm and the human intention vector, with the weight of the intention vector decaying Gaussian along the normal direction on the robot surface.

[0071] Interactive potential field The virtual potential energy distribution and potential field gradient on the robot surface are given. The direction represents the direction of the local resultant force, and its norm reflects the magnitude of the resultant force that needs to be applied. However, relying solely on the potential field gradient would cause the power density to be entirely determined by tactile geometry, failing to reflect the operator's cooperative intentions in a timely manner. This invention uses the human intention vector... By incorporating power density construction, interpretable power modulation is achieved through directional consistency dot product and normal Gaussian attenuation. The desired power density is defined as:

[0072] Represents the three-dimensional coordinates of a tiny element on the robot's surface; Indicates coordinates The interactive potential energy; This represents the gradient vector of the potential field; Represents the gradient norm of the potential field; The unit vector representing the direction of the potential field gradient; The vector representing the human intent is obtained through multimodal temporal attention pooling. Indicates the unit direction of the intent vector; Represents scalar weighting coefficients, range ; Indicates from The distance from the surface normal to the outside; Represents the normal Gaussian weight ; This represents the Gaussian decay scale.

[0073] The first term in the formula represents the pure geometric drive power density, and the second term represents the directional modulation power density, the magnitude of which is adjusted by both the gradient norm and directional consistency. Directional consistency is calculated using a unit vector dot product; if the direction aligns with the intended direction, the dot product is positive and enhances the power; if it's opposite, it attenuates or even reverses the power. Gaussian weights are used. This exponentially reduces power distribution at spatial points farther from the surface, avoiding unnecessary power consumption by deep voxels. Weighting It can adaptively adjust according to the task stage: increase the influence of intent during the teaching stage and increase the influence of geometry during the automatic following stage.

[0074] The desired power density, after discretization, is used as the source measure input entropy-normalized optimal transmission algorithm to obtain the optimal flow rate from the source to the joint capacity measure. The effect of adding an intention term to this process is reflected in three aspects: First, the power field forms a steep gradient in the operator's indicated direction, guiding a rapid response of the joint torque. Second, reverse direction movements automatically suppress power output, improving passive safety. Third, normal attenuation avoids the generation of pseudo-power in non-contact voxels, saving computational overhead and reducing energy consumption.

[0075] Example 7: A robotic arm assists an operator in moving a bellows. The distal tactile skin consists of 32×32 units. Set to 5mm, The power density was set to 0.2 during the teaching phase and increased to 0.6 during the automatic following phase. The system calculates the gradient norm and directional consistency with a period of 5ms, generates the desired power density, and then executes optimal transmission and joint advance. After 60 transport actions were tested, compared with the baseline of unintended modulation, the peak maximum torque was reduced by 6%, and the completion time of the cooperative action was shortened by 9%. Furthermore, in accidental collision scenarios, power was automatically reduced when the directional consistency was in the negative range, resulting in a 30% decrease in traction force, demonstrating that this power density construction strategy balances efficiency and safety.

[0076] Preferably, the entropy-regular optimal transport uses logarithmic field Sinkhorn iteration to update the dual variables, and its cost matrix includes lever length, joint viscous friction, and topological adjacency distance terms.

[0077] Entropy-regularized optimal transport is used in this invention to advance the desired power density from the robot surface to the joint capacity measure. Its computational efficiency and numerical stability directly affect the closed-loop control cycle. Traditional linear programming-based optimal transport is too costly to solve on high-resolution grids. To meet the control cycle of 5 milliseconds, this invention adopts an entropy-regularized form and uses Sinkhorn iteration to update the dual variable in the logarithmic domain, significantly reducing complexity and avoiding numerical underflow.

[0078] First, the source measure Representing discrete desired power density, the target measure Joint capacity; cost matrix Designed for , Indicates the source mesh To the joint The cost of transporting power per unit of power; Indicates the lever length weight; Representing the mesh in the robot's geometric model To the joint axis The length of the torque arm; Indicates the joint viscous friction weight; Indicates joint The coefficient of viscous friction; Indicates the topological adjacency weight; Representing the mesh on the joint connection diagram Connectivity clusters and joints The shortest adjacent distance between them. The objective function for entropy-regularized optimal transport is written as:

[0079] Represents the power-flow matrix; Represents the inner product of matrices; This represents the entropy regularity coefficient.

[0080] To avoid numerical collapse caused by extremely small coefficients in the standard Sinkhorn formula, this invention iterates the dual variable in the logarithmic field. The kernel matrix is ​​defined as follows:

[0081] Sinkhorn iterative update formula can be written as:

[0082]

[0083] and These are the source and target dual variables, respectively; Indicates the number of iterations. The source dual variable vector; For the target dual variable vector; is the discrete probability vector of the source measure; is the discrete probability vector of the target measure; The kernel matrix is ​​the cost matrix after entropy regularization; This is the transpose of the kernel matrix; This is the step index for the Sinkhorn iteration.

[0084] Logarithm field implementation storage and ,use The `-exp` safety operator replaces division to prevent exponent underflow. Iterate to... stop, Set to a control period of 5 milliseconds. The final power-flow matrix is: Because the multiplication and addition forms of logarithmic operations can be parallelized using SIMD instructions, each solution actually takes 0.35 milliseconds, which is only 7% of the control cycle.

[0085] Introducing a lever length term helps to geometrically shorten the lever arm and reduce the peak joint torque; a viscous friction term prompts the algorithm to prioritize joints with low friction; and a topological adjacency distance term ensures that power is preferentially transferred to joints topologically adjacent to the contact cluster, reducing energy waste from large-scale cross-chain transmission. The power flow generated after combining these three terms is more consistent with the actual robot dynamics.

[0086] Example 8: A seven-DOF robotic arm grasps a bellows, source mesh Number of joints , , The logarithmic domain Sinkhorn implementation running on a single CPU core converged after 14 iterations within the control thread. Removing the entropy regularization variant only allowed for 4 iterations but required solving a global linear programming problem, taking 8 milliseconds. Incorporating this invention reduced peak torque by 6%, energy consumption by 5%, and assembly success rate by 4%, demonstrating that the physically meaningful cost matrix and logarithmic domain iteration outperform traditional implementations in terms of real-time performance and energy efficiency.

[0087] Preferably, the parameters of the differentiable operator kernel are updated online using a recursive least squares method, and an exponential forgetting factor is used to decay the weights of old samples to improve the accuracy of joint reference torque mapping.

[0088] In the control chain of a multi-sensor collaborative robot, the optimal transmission plan obtained from power allocation must be mapped to a joint reference torque vector. Traditional methods using a fixed Jacobian matrix for advance neglect nonlinear friction, temperature drift, and compliant interface deformation, leading to accumulated mapping errors over time. This invention cascades a differentiable operator kernel after the Jacobian advance, modeling the residual mapping as an input-output operator and recursively updating it online to compensate for unmodeled dynamics. The differentiable operator kernel uses a Gaussian kernel basis function, whose output is a joint-dimensional linear operator that performs a weighted summation of the input power-flow matrix and additional quantities such as joint temperature and velocity. To adapt the kernel parameters to daily wear and assembly errors, this invention uses a recursive least squares algorithm combined with an exponential forgetting factor to estimate the weight matrix online. This strategy gradually improves advance accuracy while maintaining real-time performance, avoiding overfitting to older data.

[0089] Let the initial torque vector obtained by pushing forward be... The true torque vector obtained based on sensor observation is Define the error vector. The differentiable operator value kernel provides the error compensation term:

[0090] in Represents the torque residual compensation vector; Represents the kernel matrix, input A feature vector containing power flow elements and joint states; This represents the vector whose kernel weights are to be estimated.

[0091] The weight vector is updated using recursive least squares:

[0092]

[0093] Indicates the first The updated core weights; Indicates the first Step covariance matrix; Represents the exponential forgetting factor, with a range of values. ; Indicates the first Step feature vector; Indicates the first Step torque error.

[0094] Recursive least squares performs a matrix multiplication and addition once per control cycle. The computational complexity increases linearly with the number of joints, but can be completed within a 5-millisecond budget. An exponential forgetting factor decays historical data exponentially, reducing the influence of old samples over time and ensuring that the kernel weights quickly follow system dynamics. The compensated joint reference torque... Send it to the drive controller for execution.

[0095] Introducing a differentiable operator kernel brings three main benefits. First, online learning of residual mapping significantly reduces advance errors, maintaining torque accuracy even under conditions of wear, backlash, or temperature drift. Second, the kernel output can adaptively weight different joints, providing greater compensation for joints with large variations in friction coefficients, thus improving overall machine efficiency. Third, recursive least squares ensures consistent update sampling, and exponential forgetting prevents old, outdated data from contaminating current weights in the long term.

[0096] Example 9: Continuous screw tightening task using a 7-DOF collaborative robotic arm. Control cycle 5 milliseconds, Gaussian kernel width parameter set to 0.6, forgetting factor... A value of 0.98 was used. After 40 minutes of testing, the average torque residual decreased from 0.42 Nm using only Jacobi extrapolation to 0.24 Nm, with the maximum residual decreasing by 38%. In the high-load range where the peak torque exceeded 25 Nm, kernel compensation suppressed the residual to within 0.32 Nm, preventing driver current saturation. Compared to a static kernel with online updates disabled, the recursive least squares version maintained error stability as the temperature increased from 25°C to 45°C, demonstrating its adaptability to temperature drift caused by exponential forgetting. Experiments verified that the combination of differentiable operator-valued kernels and recursive least squares provides a lightweight and high-precision torque mapping compensation method for multi-sensor collaborative robots.

[0097] When the consistency error calculated from the joint reference torque vector, whole-body impedance command, execution state vector, interactive potential field, and system energy continuously exceeds a preset threshold, the Koopman boosting model is estimated online according to the causal weights. The model predictive control that satisfies the energy constraint, conformal safety set constraint, and topological consistency constraint is solved in the boost space. The updated joint torque and impedance commands are output, and the causal weights, conformal safety set, and updated energy Lagrange multipliers are fed back to the interactive potential field generation process and the power distribution process to form a closed-loop control.

[0098] In closed-loop operation, if there is a continuous deviation between the joint reference torque and the actual torque, or between the impedance command and the executed impedance, the coordination accuracy will be reduced and overload may be triggered. This invention sets up a consistency error monitor, and when the error sequence continuously exceeds the threshold, it initiates a Koopman-based boost replanning based on causal weights.

[0099] Consistency error is defined as:

[0100] Represents the actual torque vector; Indicates the reference torque vector; Represents the actual impedance matrix; Represents the reference impedance matrix; Indicates the trade-off coefficient; Denotes the Euclidean norm; This represents the Frobenius norm.

[0101] like In window length The value remains above the threshold. The system identifies a linear approximation mismatch, necessitating a re-identification of the dynamics. Sparse Granger causality analysis is used to select the delay features that contribute most to the torque and impedance residuals from the observation vector, generating a causal weight vector. Causal weights retain only significant terms, while the rest are set to zero, reducing the base dimension and improving the speed of online estimation.

[0102] After feature selection, the state expansion variables are... Establish a Koopman linear model:

[0103] Indicates the state of the lifting space; Represents a dictionary mapping of basis functions; Represents a linear transition matrix; Represents the control effect matrix; This indicates a control input.

[0104] Online update using weighted recursive least squares:

[0105] Represents a parameter vector; Represent the covariance matrix; The exponential forgetting factor is embedded in The recursive formula ensures that the weights of the old samples are adjusted accordingly. attenuation.

[0106] After obtaining the updated A and B, solve the model predictive control in the lift space:

[0107]

[0108]

[0109]

[0110]

[0111] Indicates a reference elevation status; Represents the weight matrix; Indicates the prediction step size; Indicates predicted energy; Indicates the upper limit of energy; The first constraint represents the conformal safety set; the second constraint represents the persistent graph operator. The third constraint is the conformal safety set constraint, and the fourth constraint guarantees topological consistency. After solving for the control sequence, the first term is taken and mapped back to the joint space to update the torque and impedance commands.

[0112] Causal weight The safety set boundary and the updated energy Lagrange multipliers are fed back to the potential field generation and power allocation processes, enabling both processes to automatically adjust their parameter ranges in the next cycle. The overall closed-loop ensures that the system can recover optimal linear prediction accuracy within several cycles when physical mismatches or external disturbances occur.

[0113] Example 10: When picking up multi-specification motor stators on an assembly line, the robot's Jacobian model error increases due to tool deformation. The robot continuously exceeded the threshold within a 40-millisecond time window. After triggering the boost, 12 key features were selected using causal weights, and a recursive least squares approach was used for convergence in 6 steps, with an update time of 0.4 milliseconds. Subsequently, the new torque output by the MPC reduced the residual by 45%, kept the peak energy within the limit, and increased the task latency by 3%, which was far less than the time required to recalibrate the model. Experiments show that this invention achieves real-time adaptive compensation through causal selection and boost control, enhancing the long-term stability and safety performance of the multi-sensor collaborative robot.

[0114] Preferably, the basis function dictionary of the Koopman boosting model is composed of a combination of quadratic polynomial basis and radial basis functions, and the model parameters are estimated in real time by least squares method with causal weight reweighting.

[0115] To address the real-time predictive control problem of collaborative robots in complex and nonlinear dynamic environments, this invention employs the Koopman boosting approach after a consistency error is triggered, mapping the original state to a high-dimensional linear evolution space. Unlike traditional methods that choose a fixed polynomial basis or radial basis functions, this invention simultaneously introduces a quadratic polynomial basis and radial basis functions, and uses causal weighting to ensure the basis dictionary balances global approximation capability and local sensitivity. This strategy guarantees the affine approximation accuracy of the Koopman linear model for a wide range of joint and end-effector states, while leveraging radial basis functions to quickly adapt to small nonlinear changes such as local friction and compliant member compression. Model parameters are estimated in real-time using a reweighted least squares algorithm, with causal weights assigning high weights only to input features strongly correlated with the consistency error, reducing noise interference and shortening numerical convergence time.

[0116] Let the robot's low-dimensional state vector be... The control input is Design Improvement Mapping:

[0117] in This indicates that the matrices are stacked column-wise as a vector; Depend on It consists of radial basis functions, forming:

[0118] Indicates the first Radial base center This represents its bandwidth. Therefore, increasing the spatial dimension is... In each control cycle, operator input features are selected based on causal weights and combined with the actual state and control input from the previous cycle to form a regression pair. .remember:

[0119]

[0120] Updated via recursive least squares:

[0121]

[0122] This indicates a promotion mapping; Represents a matrix column-heap vector; Represents the radial basis vector; Indicates the radial base center; Indicates the radial basis bandwidth; Indicates the original state dimension; Indicates the number of radial bases; Indicates the first Step-by-step regression input; Indicates the first Step up the status; Represents a parameter vector; Represent the covariance matrix; Represents the causal weight diagonal matrix; This represents the exponential forgetting factor.

[0123] Iteration size only with Since the vectors are linearly related, the process can be completed within 5 milliseconds. The updated linear model is used to predict the window. The algorithm improves the state within the loop and optimizes the input sequence at a quadratic cost, while satisfying energy upper bounds, conformal safety sets, and topological consistency constraints. The first input is mapped back to the joint space and executed in the next cycle, continuously corrected through an error loop.

[0124] The basis function dictionary employing quadratic polynomials combined with radial bases offers three advantages. First, higher-order polynomial terms provide a globally interpretable dynamic coupling structure, while radial bases capture local stiffness variations and frictional nonlinearities. Second, causal weights are applied to past... The residuals are assigned values ​​based on the Granger criterion results of the input to ensure that only high-contribution features participate in parameter updates, reducing overfitting; third, recursive least squares are combined with a forgetting factor. The influence of old samples decays exponentially, allowing for rapid reassessment after temperature drift or tool changes. Furthermore, the model maintains linear constraints in the improvement space, enabling direct integration into quadratic programming solvers for predictive control without the overhead of nonlinear solutions.

[0125] Example 11: In a complex assembly line, a robot uses a flexible end-effector to grasp parts of three different shapes. Original state dimension Radial base number The online consistency error was measured to exceed the threshold for 40 milliseconds consecutively, triggering a boosting mechanism that selected 18 causal features. The recursive least squares iteration converged in 5 steps, taking 0.37 milliseconds. After updating the model, the mean square error of the torque residual decreased from 0.46 Nm to 0.27 Nm, the maximum error was reduced by 41%, and energy utilization improved by 6%. Compared to the boosting model using only polynomial bases, in the scenario of severely deformed flexible fixtures, the polynomial + radial basis dictionary had a 15% lower average error and a 22% faster convergence speed. Experiments demonstrate that the combined dictionary of quadratic polynomials and radial basis functions, causal weight selection, and recursive least squares updates collectively ensured the real-time performance, accuracy, and adaptability of the Koopman boosting model.

[0126] Preferably, the conformal safety set is constructed based on the state residual distribution within the sliding window, taking a preset quantile radius, and the scaling factor corresponding to the radius is simultaneously applied to the joint capacity measure to ensure that the energy constraint is feasible.

[0127] In the closed-loop architecture of this invention, real-time model predictive control must ensure that the optimized trajectory falls within the dynamic safety domain. Traditional methods using fixed spherical or hyperrectangular constraints fail due to model errors and external disturbances. To address this, this invention employs a conformal safety set: utilizing the state residual distribution within a sliding window, the residual size is adaptively estimated and a shrinking set is constructed. Then, the energy budget is simultaneously tightened by scaling the joint capacity metric, achieving a balance between physical feasibility and safety.

[0128] The system has a length of Record the improvement state prediction and observation errors within the sliding window:

[0129]

[0130] in Indicates the first Step-by-step observation to improve status, Indicates the synchronous forecast value. Denote the L2 norm. Calculate the preset quantiles for the residual sequence. (For example ) Obtain the radius:

[0131] Therefore, conformal safe sets are defined as follows:

[0132] This indicates a reference lifting state. To ensure that the energy constraint tightens simultaneously, a scaling factor is introduced:

[0133] To calibrate the nominal radius. Simultaneously affects joint volume measurement:

[0134] In the formula Indicates joint Rated energy capacity, This indicates the volume after shrinkage.

[0135] Indicates the state of the lifting space; Indicates the model's predicted state; Indicates the first Residual; Indicates the length of the sliding window; Indicates quantiles; Indicates the conformal radius; Indicates a reference elevation status; Indicates the capacity scaling factor; Indicates the nominal radius; Indicates joint energy capacity; This indicates the scaled capacity.

[0136] In principle, the high quantiles of the residuals can cover 100%. Historical errors are addressed to achieve probabilistic safety guarantees; the conformal safety set is equivalent to constructing an adaptive sphere in the lift space to avoid constraint penetration caused by model drift. After scaling the joint capacity, the energy Lagrange multipliers automatically expand or contract within the quadratic programming, ensuring that the optimization problem still has feasible solutions.

[0137] In implementation, residual sequence updates and quantile queries are performed using... The linear statistical analyzer is computationally independent of the window length and can complete the task within 0.06 milliseconds. The capacity scaling factor and energy budget are synchronously written into the QP solver to ensure that the safety set is consistent with the energy constraints.

[0138] Example 12: In a rapid teaching grasping task, the addition of a flexible tool to the robotic arm's end effector increases the error in the dynamic model. The window length is set to 40, the quantile is 0.95, and the nominal radius is 0.08. Within 1 second of startup, the mean of the residual distribution is 0.05. The estimated value is 0.09, the capacity scaling factor is 1.13, and the energy budget is automatically increased by 13% to ensure that feasible trajectories can still be generated during the initial period of large errors. Once the tool stabilizes, the mean residual value decreases to 0.03. By shrinking the coefficient to 0.05, the energy limit is reduced to 0.63, thus tightening the energy limit and preventing excessive output. Statistics from 120 teaching actions show that, after adding the conformal safety set, there were no violations of the energy constraint, the peak torque decreased by 6%, and the task completion time increased by less than 2% compared to the fixed radius baseline, demonstrating the excellent trade-off between safety and efficiency achieved by the method of this invention.

[0139] Preferably, the causal weights, conformal safety sets, and updated energy Lagrange multipliers are pushed to the interactive potential field generation process and power allocation process in real time through a shared memory circular buffer to maintain data consistency within the control cycle.

[0140] In the multi-sensor collaborative robot control system of this invention, the interactive potential field generation and power allocation both operate with a 5-millisecond cycle. If the causal weights, conformal safety set radius, or energy Lagrange multipliers lag within the same cycle, inconsistent data will be used by the conditional diffusion network, entropy-normalized optimal transmission, and Koopman replanning, thereby disrupting closed-loop convergence. To ensure data consistency, this invention uses a shared memory circular buffer (hereinafter referred to as the circular buffer) to push three types of key quantities: the causal weight vector, the conformal safety set radius, and the energy Lagrange multipliers. The circular buffer is located in a high-speed dual-port static random access memory on the robot's main control board, and is directly mapped and accessed by the write end (replanning thread) and the read end (potential field / power thread) under the same bus, realizing cross-thread zero-copy communication.

[0141] The ring buffer capacity is set to Frame. Whenever the replanning thread completes an optimal control solution, the write end immediately executes the following instruction:

[0142] Indicates a write pointer. Writes to the data structure:

[0143] in Represents the causal weight vector; Represents the conformal safety radius based on quantiles; This represents the energy Lagrange multiplier. The write end then atomically updates the write pointer and triggers a memory fence to ensure data visibility. The read end reads the read pointer at the beginning of the potential field thread. :like This indicates that there is a new frame in the buffer, according to:

[0144] Complete the data retrieval; otherwise, reuse the parameters from the previous frame to avoid blocking during empty reads. Indicates the frame capacity of the circular buffer; Indicates a write pointer; Indicates reading the pointer; This represents a causal weight vector, consisting of a floating-point array of weight coefficients. The radius of the conformal safety set is obtained from the 95th quantile of the residual distribution; Represents the energy Lagrange multiplier, used for biduplex energy constraints. This represents a data frame pushed out; mod indicates modulo operation. This indicates transpose.

[0145] Both the write and read threads adhere to single-producer, single-consumer semantics, and the entire communication employs a lock-free design: only the write thread updates. Read thread updates Therefore, mutual exclusion is not required; memory barriers ensure that the pointer is written after a write operation is completed and that the data is intact before a read operation reads the pointer, avoiding false sharing. Since the frame structure length is fixed, pipelined processing is CPU cache-friendly.

[0146] To handle occasional write pointer catching up with read pointer (extreme computational tailing), the system employs an overlay strategy: the write end overwrites the oldest frame and writes the overlay flag to the monitoring register; the potential field thread detects the flag and immediately halves the diffusion steps and Sinkhorn iterations, shortening the next cycle computation and ensuring real-time recovery. Tests show that this strategy keeps the maximum latency under short-term burst loads within 8 milliseconds.

[0147] The circular buffer also handles cross-module timestamp synchronization. Each frame includes a 32-bit timestamp field. When writing, the master clock value is retrieved; when calculating the topology loss, the potential field thread compares its own timestamp with the master clock value. If the difference exceeds 250 microseconds, the comparison will be reduced. Weights are used to avoid overly strong topological constraints due to outdated parameters.

[0148] The shared memory push scheme improves system performance on three levels. First, the causal weight refresh frequency is consistent with the control cycle, synchronizing Koopman basis function selection and scoring network condition injection, reducing dynamic drift. Second, real-time push of the conformal safety radius allows model predictive control and power allocation to share the latest safety boundary, avoiding deviations in the feasible region caused by the independent expansion of different modules. Third, after the energy Lagrange multipliers are synchronized, the potential field generation can directly adjust the upper limit of the gradient norm based on the current energy budget, achieving closed-loop control before and after energy allocation.

[0149] Example 13: In a logistics palletizing application, a robot grips an 8 kg cardboard box, and the contact pattern between the flexible end gripper and the object varies greatly. The replanning thread runs on the real-time core, completing optimization in an average of 3 milliseconds. The data is pushed to the buffer. The potential field thread and power thread read at 5-millisecond cycles; no frame drops occurred during the 4-hour experiment. Compared to the Ethernet transmission scheme, the ring buffer's average latency was 110 microseconds, a reduction of 87%; the mean square value of torque consistency error decreased by 12%. At the peak error level, the dynamic overlay mechanism controlled the periodic violation rate to 0.3%, confirming that the push mechanism can operate robustly and maintain data consistency under industrial real-time control constraints.

[0150] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects.

[0151] The above are merely embodiments of this application and are not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A control method for a multi-sensor collaborative robot, characterized in that, Includes the following steps: Multimodal mechanical, tactile, visual, and physiological signals are collected, preprocessed, and time-synchronized to generate a unified observation frame. Power flow is calculated by combining joint position, joint velocity, and actual torque. The system energy is obtained by integration and an execution state vector is formed. Topological descriptors are extracted from uniform observation frames using persistent coherence. These descriptors are used as conditional inputs to a diffusion generation model, which outputs an interactive potential field and a human intention vector. The desired power density is constructed based on the gradient of the interactive potential field and the human intention vector. The power allocation plan is obtained by using entropy regularization optimal transmission. The joint reference torque vector and the whole body impedance command are generated by the Jacobian matrix and combined with the value kernel of differentiable operators. At the same time, the energy Lagrange multiplier is updated. When the consistency error calculated from the joint reference torque vector, whole-body impedance command, execution state vector, interactive potential field, and system energy continuously exceeds a preset threshold, the Koopman boosting model is estimated online according to the causal weights. The model predictive control that satisfies the energy constraint, conformal safety set constraint, and topological consistency constraint is solved in the boost space. The updated joint torque and impedance commands are output, and the causal weights, conformal safety set, and updated energy Lagrange multipliers are fed back to the interactive potential field generation process and the power distribution process to form a closed-loop control.

2. The method according to claim 1, characterized in that, The unified observation frame eliminates frequency band overlap noise through cascaded high-pass and low-pass filtering, and after denoising by time-domain moving average, the modal data are aligned to the same time using timestamps synchronized by a precision time protocol.

3. The method according to claim 1, characterized in that, The topology descriptor constructs a cubic complex by setting progressively higher thresholds on a tactile pressure grid, then calculates zero-order and first-order persistent entries, and the resulting entries are mapped to form a fixed-dimensional topology summary vector through two-dimensional meshing.

4. The method according to claim 1, characterized in that, The diffusion generation model employs a conditional diffusion probability network, whose loss function includes a homology preservation term. The homology preservation term uses the Wasserstein distance to measure the difference between the persistent graph output by the model and the topological descriptor, thereby preserving the connectivity structure of the interaction potential field.

5. The method according to claim 1, characterized in that, The desired power density is obtained by weighted summation of the dot product of the gradient norm of the interactive potential field and the human intention vector, with the weight of the intention vector decaying Gaussian along the normal direction on the robot surface.

6. The method according to claim 1, characterized in that, Entropy-regular optimal transport uses logarithmic field Sinkhorn iteration to update dual variables, and its cost matrix includes lever length, joint viscous friction, and topological adjacency distance terms.

7. The method according to claim 1, characterized in that, The parameters of the differentiable operator kernel are updated online using a recursive least squares method, and an exponential forgetting factor is used to decay the weights of old samples to improve the accuracy of joint reference torque mapping.

8. The method according to claim 1, characterized in that, The basis function dictionary of the Koopman lifting model consists of a combination of quadratic polynomial basis functions and radial basis functions. The model parameters are estimated in real time using the least squares method with causal weight reweighting.

9. The method according to claim 1, characterized in that, The conformal safety set is constructed based on the state residual distribution within the sliding window, taking a preset quantile radius, and the scaling factor corresponding to the radius is simultaneously applied to the joint capacity measure to ensure the feasibility of energy constraints.

10. The method according to claim 1, characterized in that, Causal weights, conformal safety sets, and updated energy Lagrange multipliers are pushed in real time to the interactive potential field generation and power allocation processes via a shared memory circular buffer to maintain data consistency within the control cycle.

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